Oh no, my apologies! The quotation marks are just a quirk of my writing/explaining things; I genuinely meant no offense, I just like to block out certain phrases/words in quotes for emphasis. My apologies
Historical thinking and doing history can broadly be defined as how we think of the past. Crudely divided (and albeit stereotypical, I know popular history has much more nuance than this but its not my expertise by any means), popular history understands the past as an unproblematic sequence of events, with particular moments immortalized due to their later-understood significance (think in terms of how history textbooks present them: the signing of the Magna Carta, the Ottoman conquest of Constantinople, etc framed as singular moments which irrevocably changed the course of human history, leading to the modern day). That thinking isn't necessarily wrong, but it is problematic: often it manifests in thinking of history as simply the decisions of a few great men (and, indeed, it often framed as male: for this mode of thinking, see the work of Thomas Carlyle).
Academic history is of course not immune to this impulse, but it tries to distinguish itself in adopting historical research methods (namely, critically reading, evaluating, and comparing primary sources to explain the past). For some historians, this is seen as a better alternative to popular history, as it (ostensibly) adopts an objective view of the past through a rigorous method. White's Metahistory criticizes this view in particular, leading him to argue that history writing is not a mere analysis and ordering of the past, but instead akin to a literary genre. For White, historians infuse narrative into their work, creating histories that describe the past as essentially stories but with a veneer of objectivity. This argument is controversial among some historians, but I think its an essential one to be familiar with.
Apologies for my reductionist approaches above, I can only elaborate so much in a forum post (and, admittedly, I'm hardly a historical expert).

Both deal with “historical thinking,” though both also address the institutionalization of history (in the academy). So they simultaneously address what it means to think about and “do” history in general (not as a discipline of study) while also examining history as an academic field.